Decadal evolution of GPS, GLONASS, and Galileo mean orbital elements

Abstract We examine the decadal evolution of GPS, GLONASS, and Galileo satellite orbital elements, including the semi-major axis, inclination, eccentricity, right ascension of the ascending node, and the argument of perigee. We focus on the long-term changes in Keplerian elements by averaging them over several complete revolutions forming mean orbital elements giving an explanation of the main perturbing forces for each Keplerian parameter. The combined International GNSS Service (IGS) orbits are employed which were derived in the framework of IGS Repro3 for ITRF2020 preparation spanning eight years from 2013 to 2021. The semi-major axis for GPS satellites is affected by a strong resonance with Earth’s gravity field resulting in a long-period perturbation similar to a secular drift. The semi-major axes of Galileo and GLONASS do not show any large-scale rates, however, Galileo satellites are affected by the Y-bias resulting in semi-major axis drifts. A significant perturbations due to solar radiation pressure affect the semi-major axis, eccentricity, and the argument of perigee. Notably, for Galileo satellites in eccentric orbits, the signal with a one-draconitic year is evident in the semi-major axis. The evolution of the mean right ascension of the ascending node and argument of perigee is primarily characterized by nearly linear regression mainly due to even zonal harmonics of the Earth’s gravity field. The long-term evolution of eccentricity and inclination does not follow a linear trend but exhibits clear oscillations dependent on the secular drift of the right ascension of the ascending node (for inclination) or the argument of perigee (for eccentricity). Additionally, the long-term perturbation of inclination reaches its maximum when the absolute value of the Sun’s elevation angle above the orbital plane ( $$\beta$$ angle) is at its minimum, while the eccentricity reaches its minimum simultaneously with the minimum of the $$\beta$$ angle.